It will be seen that the commission is at the rate of nearly 4 per-cent on the premium income, and that the commission and expenses of management amount together to 134 per-cent on the premium income. Taking the average results of the 15 offices, we obtain figures which may perhaps be more useful than the large totals in the statement. We have then :

Now let us consider what is the rate of expenditure at which a company of this size could be managed, irrespective entirely of new business.

This is equal to about 7 per-cent on the renewal premium income. Deducting £12,000 from £24,177 (the total amount of expenses and commission), there remains the sum of £12,177, which is applicable to the new business of £507,650. This yields a rate of £2. 7s. 11d. on each £100 assured. The average age at entry being about 40, and the average premium on a whole-life assurance being therefore about £3, this represents an expenditure in acquiring the business of 80 per-cent of the first year's premium. Add to this the risk of the first year, which by the Institute experience, HM first year of assurance, is, at the average age at entry, about 10s., and we find a sum of £2. 17s.. 11d. per £100 assured, or 96 per-cent of the first year's premium expended on the year's risk and expenses. We see, therefore, that in the case of the Scottish offices the whole of the first year's premium is swallowed up in claims and expenses, and thereafter the expenditure is 74 percent on the premium income. This may not be the most desirable state of matters. It would of course be preferable if business

could be obtained at a lower rate of expenditure; but the state of matters exists, and it cannot be made worse by being faced.

In the case of offices whose expenditure resembles that described above, the question necessarily arises as to the mode in which this expenditure is to be provided for in the construction of the premiums. It is usual to consider the premium as consisting of two unequal parts, the larger being the mathematical, pure, or net premium, and the smaller being the loading, or addition for expenses, contingencies, and profit. In the case of non-participating assurances, the loading is generally an equal percentage on the mathematical premium at all ages; occasionally, however, the addition is made in the form of a constant and a percentage. In the case of assurances intended to participate in the profits, there is a larger addition, usually regulated in some measure by the bonus system of the office and the prospects of profit which it holds out to entrants at the various ages. Though the amount of the annual loading may differ at each age at entry, it is, I believe, invariably treated in this country in practice as of the same amount during the first year as during the subsequent years of the existence of the policy. Why should this be so, if it does not correspond with the manner in which the expenses are incurred?

Leaving out of account the additions for profit and for contingencies, let us assume that an addition of about 15 per-cent on the mathematical premium is usually added for expenses, equal perhaps to about 13 per-cent on the gross non-profit rates, or 11 per-cent on the gross participating rates. This is probably not far from the mark; and the resulting average rate on the whole premiums (participating and non-participating) will probably be about 11 per-cent. It may be the case that taking an average duration of policy, the 11 per-cent per annum is exactly equal in value at the outset to the rate of 79 per-cent on the first premium, with 7 per-cent on renewals, which we have seen represents something like the average rate of expenditure in the case of a class of offices employing agents and district managers; but this fact does not show that it is a matter of indifference whether the provision for expenses is made in the one form or the other. Assuming that at the outset the value of the expenses, according to fact and according to hypothesis, are equal; at the end of the first year, after all the preliminary expenses have been paid, the values of the future expenses differ widely by the two methods.

The actual future expenses are 7 per-cent, while the proportion reserved by the ordinary method is 11 per-cent, or nearly 50

per-cent too much; while in the case of past expenses the proportion allotted by the hypothesis is only 11 per-cent, as compared with 80 per-cent of actual expenditure.

The unsuitableness, theoretically, of the ordinary net premium method of valuation to an office which transacts its business in the ordinary manner, becomes evident when we consider that by this method at the end of one year a reserve is required of nearly 50 per-cent, on the average, of the amount of the first year's premium. If 79 per-cent be spent in acquiring the business, and 21 per-cent in meeting the first year's risk, whence is the additional 50 percent to be derived? If the company is a proprietary one, and has been only one year in existence, the deficiency must be made up from the capital or from the interest on the capital. In the case, however, of a mutual office, there is no fund at the outset from which this deficiency can be made up: and in such a case, if the ordinary net premium system be correct, the office must be unable to meet its liabilities! And yet the present value of the gross future premiums, under deduction of 7 per-cent, is probably far more than equal to the present value of the sums assured. In such a case it would be absurd to say that the office is insolvent. The first year's contract has been fulfilled; and all expenses have been paid, without in any way encroaching on the provision for future expenses and claims, which will be amply met by the future premiums. We are therefore driven to disregard the result of the net premium valuation, and to seek for some other method less inconsistent with fact.

The method which seems most suitable to such circumstances is that proposed by Mr. Sprague in his paper "On the Proper Method of Estimating the Liability of a Life Insurance Company under its Policies", which appeared in the Journal of the Institute of Actuaries for July 1870. This is-To reserve for policies in their first year only sufficient to meet the unexpired current risk, and to consider that all policies of more than one year's standing have been effected at the next higher age, the expression for the value of a policy on this plan being

Ax+n—(1+αx+n)@x+1·

By this plan every year pays its way, and the principal advantages of both the net and gross premium systems are retained. As compared with the ordinary gross premium system of valuation, this plan is greatly to be preferred, as it does not create, in the case of the more recent policies, an apparent asset, which may at any

time be rendered valueless by the policies being dropped, -the future margin, which was wholly or partially reckoned on, being lost to the company.

This must conclude the present paper. I had intended to give illustrations showing the importance of testing, not only the amounts of new business produced by the various means employed, but also the permanency of the business thus obtained; and I had also proposed to myself to show how, owing to the mortality profit derived from the introduction of a large new business, and from other causes, the unsuitableness of the ordinary net-premium methods of valuation is partially neutralized, or at all events concealed, in the case of offices which have already a large existing business. These points, however, must be left to a future paper.

Does a Large New Business benefit the Policyholders of a Life Company? By JAMES R. MACFADYEN, of the Legal and General Life Assurance Society.

[Extracted from the Insurance Times of New York.]

THE question with which I have headed this paper is one that may seem startling enough. It has been so widely taken for granted that a large new business must be an unmixed good to all concerned in a life company, that to debate whether it be so or no, will seem in the eyes of many to be a very idle thing. And yet, though I have been considering the subject for a long time, I cannot answer the question unhesitatingly in the affirmative. In saying this, it ought to be pointed out, that the matter is regarded from a purely practical point of view. The problem is not ought a large new business to benefit policyholders? but, as a matter of fact, does it? Even if the question were answered in the negative, it would not follow that no new business, or an insufficient quantity of it, would better suit the interests of the policyholders. Waste must be supplied, and a certain degree of magnitude maintained in life companies.

Though attempting to analyze the matter from a practical point of view, I do not propose to take the bonuses already declared by the various societies into consideration. No doubt to a "withprofit" policyholder the bonus is in this matter the sole measure

of the benefit he may get in one office more than in another. And no doubt, also, it is the "with-profit" policyholder alone that is concerned with the answer to the question heading this paper; because, to make comparison between life companies possible, we must assume that each is solvent, and that each offers conditions of assurance alike liberal. But still, while admitting all this, I do not think it necessary or safe to make the declared bonus of offices one of the elements to be taken into account in discussing the matter. It is not necessary, because the subject can be dealt with thoroughly at the source and fountain head of all bonus, namely, the premiums payable. It is not safe, because bonus is partially dependent on the actuarial basis; and this new factor in our calculations will interfere sadly with our comparisons. In an assurance office, the past bonus is no index of the future. Even were the actuarial basis of each company under examination the same, comparisons of the bonus, as the measure of profit to policyholders in the various societies, would still be hazardous. The system of division of surplus employed may be of such a character as to render declared bonus an unsafe ground of comparison of the individual office with other companies, or even with itself at former periods of its existence. If realized profit is to form an element in the discussion at all, the bonus-producing power of the various companies should be the standard of measurement. But, as I have already said, it seems unnecessary to bring the bonus into the discussion of the matter at all.

In treating as to whether a very large or a somewhat smaller new business is the more remunerative to those connected with a life company, I shall do so purely from the policyholder's point of view. There is, I think, no question but that a large business, if not absolutely unprofitable, is, to the shareholders and officials of a life office, emphatically a good thing; but it is not so clear that a policyholder is benefited by it. So far as he is concerned, the fact that the larger societies make a greater amount of profit, won't settle the question in their favor; for it has to be divided among a correspondingly greater number. I say correspondingly", because we cannot assume that in its larger new business the greater office has a disproportionate excess of non-participating

assurances.

There are only two sources from which a policyholder can reap any advantage in a large over what he could obtain in a smaller company. The one is, there will be less violent fluctuations in the first class of offices, in consequence of their greater number of